Some philosophers say it is mathematicians’ work while some mathematicians say it is philosophers’ work.

Is that the very reason “why infinite related mathematical paradox families have been challenging human for more than 2500 years”? 

Dear Geng Ouyang,

Interesting question… But I do not know what is its practical importance (stimulate your brain for resolving other importance question)  It would be preferable for the student between 20-27 years… Laozi example also gave response to such a question…

More important seems:  which science appeared before: mathematic or Philosophy … I think the mathematics: when the owner determined its rise quantity for verifying wanted to know if somebody it stole it or not… Philosophy-religion after it when he realised that somebody had stolen from his rise!

Best Regards,

László   

In fact, the quantitative cognition segment of "infinite things" has a lot to do with philosophy because the work is in the field of mathematics foundation.

Asking this question already presupposes that there are meaningful definitions of two distinct “activities”: Philosophical “activity” and Mathematical “activity”. Such presupposition is not warranted. For example, topics in Set Theory or Formal Axiomatics are certainly topics in Mathematics, but who would say that logic and axiomatic method are not in the domain of Philosophy?

Likewise, infinite numbers (infinitesimals) are rigorously defined by mathematicians (for example, Hilbert, Dedekind, Cauchy).  On the other hand, other mathematicians such as Kronecker, Weyl, Brouwer have different understanding of infinity based on philosophic considerations (Finitism). And how would you classify Kurt Gödel? His Incompleteness Theorems are certainly Philosophy, but Gödel numbering is just as certainly mathematics.

Therefore, the answer to the question about infinities and infinitesimals falling under “philosophy or mathematics” depends on your understanding of the meaning of “philosophy” and “mathematics”.

 Thank you for your insightful ideas and sharing, dear Dr. David Vogel.

I agree with you that Philosophy and Mathematics are very closely related. But I think for Philosophy work, it is more abstract than Mathematics; while for Mathematics work, it is more concreteness than Philosophy. For example: for Philosophy, it is enough to say “A is heavier than B” but for Mathematics we need to say “A is 9576 grams heavier than B”.

It is more typical in Harmonic Series Paradox: for Philosophy, it is enough to say “we are able to produce infinite items each bigger than 1/2, or 100, or 1000000, or 1000000000000000000,…by brackets-placing rule with limit theory from Un--->0 items in Harmonic Series and change Harmonic Series into an infinite series with infinite items each bigger than any positive constants (such as 100000000000000000000000000000)”; but for Mathematics we need to know “how many Un--->0 items in Harmonic Series we use to produce the first positive constants (such as 100000000000000000000000000000) and how many for the second ”.

Thank you again! 

Yours,  

Geng Ouyang

Five of my published papers have been up loaded onto RG to answer such questions:

1，On the Quantitative Cognitions to “Infinite Things” (I)

https://www.researchgate.net/publication/295912318_On_the_Quantitative_Cognitions_to_Infinite_Things_I

2，On the Quantitative Cognitions to “Infinite Things” (II)

https://www.researchgate.net/publication/305537578_On_the_Quantitative_Cognitions_to_Infinite_Things_II

3，On the Quantitative Cognitions to “Infinite Things” (III)

https://www.researchgate.net/publication/313121403_On_the_Quantitative_Cognitions_to_Infinite_Things_III

4 On the Quantitative Cognitions to “Infinite Things” (IV)

https://www.researchgate.net/publication/319135528_On_the_Quantitative_Cognitions_to_Infinite_Things_IV

5 On the Quantitative Cognitions to “Infinite Things” (V)

https://www.researchgate.net/publication/323994921_On_the_Quantitative_Cognitions_to_Infinite_Things_V